Skip to main content
main-content
Top

About this book

This Springer Handbook of Metrology and Testing presents the principles of Metrology – the science of measurement – and the methods and techniques of Testing – determining the characteristics of a given product – as they apply to chemical and microstructural analysis, and to the measurement and testing of materials properties and performance, including modelling and simulation.

The principal motivation for this Handbook stems from the increasing demands of technology for measurement results that can be used globally. Measurements within a local laboratory or manufacturing facility must be able to be reproduced accurately anywhere in the world.

The book integrates knowledge from basic sciences and engineering disciplines, compiled by experts from internationally known metrology and testing institutions, and academe, as well as from industry, and conformity-assessment and accreditation bodies.

The Commission of the European Union has expressed this as there is no science without measurements, no quality without testing, and no global markets without standards.

Table of Contents

Frontmatter

Fundamentals of Metrology and Testing

Frontmatter

1. Introduction to Metrology and Testing

Abstract
This chapter reviews the methodologies of measurement and testing. It gives an overview of metrology and presents the fundamentals of materials characterization as a basis for
1.
Chemical and microstructural analysis
 
2.
Materials properties measurement
 
3.
Materials performance testing
 
which are treated in parts B, C, and D of the handbook.
Horst Czichos

2. Metrology Principles and Organization

Abstract
This chapter describes the basic elements of metrology, the system that allows measurements made in different laboratories to be confidently compared. As the aim of this chapter is to give an overview of the whole field, the development of metrology from its roots to the birth of the Metre Convention and metrology in the 21st century is given.
Andrew Wallard

3. Quality in Measurement and Testing

Abstract
Technology and todayʼs global economy depend on reliable measurements and tests that are accepted internationally. As has been explained in Chap. 1, metrology can be considered in categories with different levels of complexity and accuracy.
  • Scientific metrology deals with the organization and development of measurement standards and with their maintenance.
  • Industrial metrology has to ensure the adequate functioning of measurement instruments used in industry as well as in production and testing processes.
  • Legal metrology is concerned with measurements that influence the transparency of economic transactions, health, and safety.
All scientific, industrial, and legal metrological tasks need appropriate quality methodologies, which are compiled in this chapter.
Michael H. Ramsey, Stephen L.R. Ellison, Horst Czichos, Werner Hässelbarth, Hanspeter Ischi, Wolfhard Wegscheider, Brian Brookman, Adolf Zschunke, Holger Frenz, Manfred Golze, Martina Hedrich, Anita Schmidt, Thomas Steiger

Chemical and Microstructural Analysis

Frontmatter

4. Analytical Chemistry

Abstract
Measurements of the chemical compositions of materials and the levels of certain substances in them are vital when assessing and improving public health, safety and the environment, are necessary to ensure trade equity, and are required when monitoring and improving industrial products and services. Chemical measurements play a crucial role in most areas of the economy, including healthcare, food and nutrition, agriculture, environmental technologies, chemicals and materials, instrumentation, electronics, forensics, energy, and transportation.
This chapter presents a broad overview of the analytical techniques that can be used to perform the higher order chemical characterization of materials. Techniques covered include mass spectrometry, molecular spectrometry, atomic spectrometry, nuclear analytical methods, chromatographic methods and classical chemical methods.
For each technique, information is provided on the principle(s) of operation, the scope of the technique, the nature of the sample that can be used, qualitative analysis, traceable quantitative analysis, and key references. Examples of representative data are provided for each technique, where possible.
Willie E. May, Richard R. Cavanagh, Gregory C. Turk, Michael Winchester, John Travis, Melody V. Smith, Paul DeRose, Steven J. Choquette, Gary W. Kramer, John R. Sieber, Robert R. Greenberg, Richard Lindstrom, George Lamaze, Rolf Zeisler, Michele Schantz, Lane Sander, Karen W. Phinney, Michael Welch, Thomas Vetter, Kenneth W. Pratt, John H. J. Scott, John Small, Scott Wight, Stephan J. Stranick, Ralf Matschat, Peter Reich

5. Nanoscopic Architecture and Microstructure

Abstract
The methods compiled in this chapter are important in many areas of materials science and technology because various physical properties of materials (mechanical, thermal, electronic, optical, magnetic, dielectric, biological) depend on their geometric architecture, on scales ranging from the atomic or nanoscopic to the semimicroscopic. Some of the properties are governed only by an elementary atomic group in the structural hierarchy while others are brought about by cooperative functioning of multiple phases or microscopic structures in different dimensions. Corresponding to the vast variety of materials and their properties, a wide range of experimental techniques are available, so that the choice of which technique to employ on starting a study may not be clear. In this respect one should also bear in mind that some of the techniques presented in this chapter are based on physical principles, which are also relevant to the measurement methods compiled in Chaps. 6 and 11.
Koji Maeda, Hiroshi Mizubayashi

6. Surface and Interface Characterization

Abstract
While the bulk material properties treated in Part C of this handbook are obviously important, the surface characteristics of materials are also of great significance. They are responsible for the appearances of materials and surface phenomena, and they have a crucial influence on the interactions of materials with gases or fluids (in corrosion, for example; Chap. 12), contacting solids (as in friction and wear; Chap. 13) or biospecies (Chap. 14), and materials–environment interactions (Chap. 15). Surface and interface characterization have been important topics for very many years. Indeed, it was known in antiquity that impurities could be detrimental to the quality of metals, and that keying and contamination were important to adhesion in architecture and also in the fine arts. In contemporary technologies, surface modification or functional coatings are frequently used to tailor the processing of advanced materials. Some components, such as quantum-well devices and x-ray mirrors, are composed of multilayers with individual layer thicknesses in the low nanometer range. Quality assurance of industrial processes, as well as the development of advanced surface-modified or coated components, requires chemical information on material surfaces and (buried) interfaces with high sensitivity and high lateral and depth resolution. In this chapter we present the methods applicable to the chemical and physical characterization of surfaces and interfaces.
This chapter covers the three main techniques of surface chemical analysis: Auger electron spectroscopy (AES), x-ray photoelectron spectroscopy (XPS), and secondary ion mass spectrometry (SIMS), which are all still rapidly developing in terms of instrumentation, standards, and applications. AES is excellent for elemental analysis at spatial resolutions down to 10 nm, and XPS can define chemical states down to 10 μm. Both analyze the outermost atom layers and, with sputter depth profiling, layers up to 1 μm thick.
Dynamic SIMS incorporates depth profiling and can detect atomic compositions significantly below 1 ppm. Static SIMS retains this high sensitivity for the surface atomic or molecular layer but provides chemistry-related details not available with AES or XPS. New reference data, measurement standards, and documentary standards from ISO will continue to be developed for surface chemical analysis over the coming years.
The chapter also discusses surface physical analysis (topography characterization), which encompasses measurement, visualization, and quantification. This is critical to both component form and surface finish at macro-, micro-, and nanoscales. The principal methods of surface topography measurement are stylus profilometry, optical scanning techniques, and scanning probe microscopy (SPM). These methods, based on acquiring topography data from point-by-point scans, give quantitative information on surface height with respect to position. The integral methods, which are based on a different approach, produce parameters that represent some average property of the surface under examination. Measurement methods, as well as their application and limitations, are briefly reviewed, including standardization and traceability issues.
Martin Seah, Leonardo De Chiffre

Materials Properties Measurement

Frontmatter

7. Mechanical Properties

Abstract
Materials used in engineering applications as structural components are subject to loads, defined by the application purpose. The mechanical properties of materials characterize the response of a material to loading.
The mechanical loading action on materials in engineering applications may be static or dynamic and can basically be categorized as tension, compression, bending, shear, and torsion. In addition, thermomechanical loading effects can occur (Chap. 8). There may also be gas loads from the environment, leading to gas/materials interactions (Chap. 6) and to transport phenomena such as permeation and diffusion.
The mechanical loading action and the corresponding response of materials can be illustrated by the well-known stress–strain curve (for definition see Sect. 7.1.2). Its different regimes and characteristic data points characterize the mechanical behavior of materials treated in this chapter in terms of elasticity (Sect. 7.1), plasticity (Sect. 7.2), hardness (Sect. 7.3), strength (Sect. 7.4), and fracture (Sect. 7.5). Methods for the determination of permeation and diffusion are compiled in Sect. 7.6.
Sheldon M. Wiederhorn, Richard J. Fields, Samuel Low, Gun-Woong Bahng, Alois Wehrstedt, Junhee Hahn, Yo Tomota, Takashi Miyata, Haiqing Lin, Benny D. Freeman, Shuji Aihara, Yukito Hagihara, Tetsuya Tagawa

8. Thermal Properties

Abstract
If materials – solids, liquids or gases – are heated or cooled, many of their properties change. This is due to the fact that thermal energy supplied to or removed from a specimen will change either the kinetic or the potential energy of the constituent atoms or molecules. In the first case, the temperature of the specimen is changed, since temperature is a measure of the average kinetic energy of the elementary particles of a sample. In the second case, e.g. the binding energy of these particles is altered, which may cause a phase transition.
Thermal properties are associated with a material-dependent response when heat is supplied to a solid body, a liquid, or a gas. This response might be a temperature increase, a phase transition, a change of length or volume, an initiation of a chemical reaction or the change of some other physical or chemical quantity.
Basically, almost all of the other materials properties treated in Part C, namely mechanical, electrical, magnetic, or optical properties, are temperature-dependent (except a material that is especially designed to be resistant to temperature variations). For example, temperature influences mechanical hardness, electrical resistance, magnetism, or optical emissivity. Temperature is also of importance to the characterization of material performance (Part D) as it influences materials integrity when subject to corrosion, friction and wear, biogenic impact or material–environment interactions. Temperature effects related to these areas are dealt with in the other chapters of this book dedicated to those topics. Only if those properties are needed to explain measuring methods within this chapter are they are outlined in the following sections.
In this chapter, a number of materials properties are selected and called thermal properties, where the effect of thermal energy treatment plays the major role compared to electrical, magnetic, chemical or other effects. The presentation of measurement methods for thermal properties is organized into five parts, referring to:
1.
Thermal transport properties, such as thermal conductivity, thermal diffusivity or specific heat capacity, characterizing the ability of materials to conduct, transfer, store and release heat.
 
2.
Phase transitions and chemical reactions of materials. Various calorimetric methods are presented, which are used to investigate e.g. phase transitions, adsorption, and mixing processes. Typical examples are first-order transitions such as boiling and melting, but also combustion and solution processes.
 
3.
Physical properties, which are affected when heat is supplied to a body. The determination of the temperature dependence of these quantities requires knowledge of thermal measurement methods. Among the many different physical quantities the most important for applications in materials science and engineering are length and its relation to thermal expansion.
 
4.
Thermogravimetry, which is important in chemical analysis, see Chap. 4.
 
5.
Temperature measurement methods, since these techniques are essential for all the other measurements described above. Temperature scales and the principles, types and applications of temperature sensors are compiled.
 
Wolfgang Buck, Steffen Rudtsch

9. Electrical Properties

Abstract
Electronic materials – conductors, insulators, semiconductors – play an important role in todayʼs technology. They constitute electrical and electronic devices, such as radio, television, telephone, electric light, electromotors, computers, etc. From a materials science point of view, the electrical properties of materials characterize two basic processes: electrical energy conduction (and dissipation) and electrical energy storage.
  • Electrical conductivity describes the ability of a material to transport charge through the process of conduction, normalized by geometry. Electrical dissipation comes as the result of charge transport or conduction. Dissipation or energy loss results from the conversion of electrical energy to thermal energy (Joule heating) through momentum transfer during collisions as the charges move.
  • Electrical storage is the result of charge storing energy. This process is dielectric polarization, normalized by geometry to be the material property called dielectric permittivity. As polarization occurs and causes charges to move, the charge motion is also dissipative.
In this chapter, the main methods to characterize the electrical properties of materials are compiled. Sections 9.2 to 9.5 describe the measuring methods under the following headings
  • Electrical conductivity of metallic materials
  • Electrolytical conductivity
  • Semiconductors
  • Dielectrics.
As an introductory overview, in Sect. 9.1 the basic categories of electrical materials are outlined in adopting the classification and terminology of the chapter Electronic Properties of Materials of Understanding Materials Science by Hummel [1].
Bernd Schumacher, Heinz-Gunter Bach, Petra Spitzer, Jan Obrzut, Steffen Seitz

10. Magnetic Properties

Abstract
Magnetic materials are one of the most prominent classes of functional materials, as introduced in Sect. 1.3. They are mostly inorganic, metallic or ceramic in nature and typically multicomponent when used in applications (e.g. alloys or intermetallic phases). Their structure can be amorphous or crystalline with grain sizes ranging from a few nanometers (as in high-end nanocrystalline soft magnetic materials) to centimeters (as in grain-oriented transformer steels). They are available as powders, cast, sintered or composite materials, ribbons or even thin films and find a huge variety of applications in transformers, motors, generators, medical system sensors, and microelectronic devices.
The aim of this chapter is to give advice as to which methods are most applicable to determine the characteristic magnetic properties of any of the materials mentioned above. Magnetic thin-film structures have recently gained significant scientific and economic importance. Not only can their properties deviate from the respective bulk materials but novel phenomena can also occur, such as giant and tunnel magneto-resistance, which lead to their application in read heads and their likely future application to nonvolatile magnetic solid-state memory (MRAM). Therefore, we have added a section that explains the important peculiarities special to thin films, in which we summarize the most relevant measurement techniques.
Section 10.1 will give a short overview to enable the reader to differentiate between the various manifestations of magnetism, different materials and their related properties. For a deeper understanding, of course, textbooks should be used (see the references given in Sect. 10.2). Section 10.2 covers the standard measurement techniques for soft and hard magnetic materials. The tables at the beginning of Sect. 10.2.1 are a valuable guide to choose the best technique for any given property to be measured. It is anticipated that this chapter will cover theoverwhelming needs for a routine characterization of soft and hard magnetic materials in their various forms. Section 10.3 introduces an elegant, novel and extremely fast technique, the so-called pulse field magnetometer, to measure the hysteresis loop of hard magnetic materials and thereby to determine the remanent magnetization, the anisotropy field and coercivity, respectively. This method has been developed only recently and is not yet comprehensively covered in textbooks. It is therefore described in more detail with a critical discussion of possible measurement errors and calibration requirements. Finally, as mentioned above, Sect. 10.4 addresses features peculiar to magnetic thin films and recommends techniques for their magnetic characterization. It comprises an overview of magneto-resistive effects occurring in magnetic thin films or multilayers where the electrical resistivity depends on external magnetic fields. These devices find important applications as read heads in hard-disc drives and as sensors in the automotive and automation industries. The standard measurement to determine the field response (change in resistance within a given field range) is simply a resistivity measurement, as described in Chap. 9, except that it needs to be done in an external magnetic field. These electrical techniques are therefore not covered in this chapter.
In bulk and thin-film ferromagnets properties such as remanent magnetization and coercivity often depend on the time scale used in the measurement (Sects. 10.1.6, 10.3.3). Time-dependent measurements needed, e.g., to predict the stability of the material in applications are not explicitly described in this chapter since, in principle, any sensitive magnetometer can be used for these measurements. In research, sophisticated methods are used to resolve magnetization dynamics on pico- or even femtosecond time scales. A detailed description of these more specialized methods is beyond the scope of this handbook.
Joachim Wecker, Günther Bayreuther, Gunnar Ross, Roland Grössinger

11. Optical Properties

Abstract
At present, optical measurement methods are the most powerful tools for basic and applied research and inspection of the characteristic properties of a variety of materials, especially following the development of lasers and computers. Optical measurement methods are widely used for optical spectroscopy including linear and nonlinear optics and magneto-optics, conventional and unconventional optical microscopy, fiber optics for passive and active devices, optical recording for CD/DVD and MO disks, and various kinds of optical sensing.
In this chapter, as an introduction to the following sections, the concept and fundamentals of optical spectroscopy are described in Sect. 11.1, including optical measurement tools such as light sources, detectors and spectrometers, and standard optical measurement methods such as reflection, absorption, luminescence, scattering, etc. A short summary of laser instruments is also included. In Sect. 11.2 the microspectroscopic methods that have recently become quite useful for nano-science and nano-technology are described, including single-dot/molecule spectroscopy, near-field optical spectroscopy and cathodo-luminescence spectroscopy using scanning electron microscopes. In Sect. 11.3 magneto-optics such as Faraday rotation is introduced and the superlattice of semi-magnetic semiconductors is applied for the imaging measurement of magnetic flux patters of superconductors as an example of spintronics. Section 11.4 is devoted to fascinating subjects in laser spectroscopy, such as nonlinear spectroscopy, time-resolved spectroscopy and THz spectroscopy. In Sect. 11.5 fiber optics is summarized, including transmission properties, nonlinear optical properties, fiber gratings, photonic crystal fibers, etc. In Sect. 11.6 optical recording technology for high-density storage is described in detail, including the measurement methods for the characteristic properties of phase-change and magneto-optical materials. Finally, in Sect. 11.7 a variety of optical sensing methods are described, including the measurement of distance, displacement, three-dimensional shape, flow, temperature and, finally, the human body for bioscience and biotechnology.
This chapter begins with a section on basic technology for optical measurements. Sections 11.211.4 deal with advanced technology for optical measurements. Finally Sects. 11.511.7 discuss practical applications to photonic devices.
Tadashi Itoh, Tsutomu Araki, Masaaki Ashida, Tetsuo Iwata, Kiyofumi Muro, Noboru Yamada

Materials Performance Testing

Frontmatter

12. Corrosion

Abstract
Corrosion is defined as the interaction between a metal and its environment that results in changes in the properties of the metal, and which may lead to significant impairment of the function of the metal. In most cases the interaction between the metal and the environment is an electrochemical reaction where thermodynamic and kinetic considerations apply. Depending on the characteristics of the corrosion system various types of corrosion occur.
In this chapter all test methods available today are described. For scientific purposes as well as investigations in the laboratory so called conventional electrochemical test methods with direct current are primarily used (Sect. 12.1). In addition, newer techniques have been proposed (Sect. 12.1) that are based on dynamic system analysis (Sect. 12.2.1) or that allow study of corrosion processes in situ with spatial resolution down to 20 μm (Sects. 12.2.2 and 12.2.3). In the following sections a distinction has been made between testing for performance of corrosion protection measures such as inhibitors (Sect. 12.8) and testing that focuses on specific types of corrosion. In this context it is advisable to differentiate between corrosion without (Sect. 12.4) and with mechanical loading (Sect. 12.5) including hydrogen-assisted cracking (Sect. 12.8) which has some similarities to stress corrosion. High-temperature corrosion (Sect. 12.6) has a different mechanistic background than electrolytic corrosion because it is a corrosion process at a metal/gas or metal/salt interface. Exposure and on-site testing (monitoring) require specific considerations in the design of test facilities, probes and the interpretation of results (Sect. 12.4).
Another important source of information regarding corrosion testing is that edited by Baboian [12.1].
Bernd Isecke, Michael Schütze, Hans-Henning Strehblow

13. Friction and Wear

Abstract
Almost all mechanical systems, artificial or natural, involve the relative motion of solid components. Wherever two surfaces slide or roll against each other, there will be frictional resistance, and wear will occur. The response of materials to this kind of interaction, often termed tribological, depends not only on the precise nature of the materials, but also on the detailed conditions of the contact between them and of the motion. Friction and wear are system responses, rather than material properties. The measurement of tribological behavior therefore poses particular challenges, and a keen awareness of the factors that influence friction and wear is essential.
This chapter provides definitions of the key concepts in Sect. 13.1, and provides a rationale for the design and selection of test methods in Sect. 13.2. Various standard and other tribological test methods are comprehensively reviewed in Sect. 13.3, which is followed by descriptions of methods used for the quantitative assessment of both friction (Sect. 13.4) and wear (Sect. 13.5). Methods used for characterizing worn surfaces and wear debris are addressed in Sect. 13.6.
Ian Hutchings, Mark Gee, Erich Santner

14. Biogenic Impact on Materials

Abstract
Materials as constituents of products or components of technical systems rarely exist in isolation and many must cope with exposure in the natural world. This chapter describes methods that simulate how a material is influenced through contact with living systems such as microorganisms and arthropods. Both unwanted and desirable interactions are considered. This biogenic impact on materials is intimately associated with the environment to which the material is exposed (Materials-Environment Interaction, Chap. 15). Factors such as moisture, temperature and availability of food sources all have a significant influence on biological systems. Corrosion (Chap. 12) and wear (Chap. 13) can also be induced or enhanced in the presence of microorganisms. Section 14.1 introduces the categories between desired (biodegradation) and undesired (biodeterioration) biological effects on materials. It also introduces the role of biocides for the protection of materials. Section 14.2 describes the testing of wood as a building material especially against microorganisms and insects. Section 14.3 characterizes the test methodologies for two other groups of organic materials, namely polymers (Sect. 14.3.1) and paper and textiles (Sect. 14.3.2). Section 14.4 deals with the susceptibility of inorganic materials such as metals (Sect. 14.4.1), concrete (Sect. 14.4.2) and ceramics (Sect. 14.4.3) to biogenic impact. Section 14.5 treats the testing methodology concerned with the performance of coatings and coating materials. In many of these tests specific strains of organisms are employed. It is vital that these strains retain their ability to utilize/attack the substrate from which they were isolated, even when kept for many years in the laboratory. Section 14.6 therefore considers the importance of maintaining robust and representative test organisms that are as capable of utilizing a substrate as their counterparts in nature such that realistic predictions of performance can be made.
Ina Stephan, Peter D. Askew, Anna A. Gorbushina, Manfred Grinda, Horst Hertel, Wolfgang E. Krumbein, Rolf-Joachim Müller, Michael Pantke, Rüdiger (Rudy) Plarre, Guenter Schmitt, Karin Schwibbert

15. Material–Environment Interactions

Abstract
There is no usage of materials without interaction with the environment. Material–environment interactions are relevant for all types of materials, be they of inorganic or organic in origin. Interactions with the environment can cause damage to materials but also might lead to an improvement of materials properties (e.g. oxidative passivation of aluminium or patina formation on copper surfaces). Interactions with the environment might also occur prior to the usage of materials, i.e. in the production phase. For example, before steel can be used for manufacturing of metal products, iron ore has to be extracted and processed.
The impact of the environment on the processes of the materials cycle (Fig. 1.15) will be discussed in Sect. 15.1.1 of this chapter. An important material–environment interaction, especially for inorganic materials, is corrosion, which has already been addressed in Chap. 12. Also the biological impact on organic and inorganic materials can be manifold and are presented in Chap. 14. Environmental mechanisms that impair the functioning of organic polymeric materials – such as weathering, ultraviolet (UV) radiation, moisture, temperature and high-pH environments – are the topics of Sect. 15.1.2. The influence of materials on the indoor climate and measurement methods to characterize emissions from materials are treated in Sect. 15.2. Fire exhibits a drastic impact on materials; methods to characterize the flammability and fire behavior of materials are discussed in Sect. 15.3.
Franz-Georg Simon, Oliver Jann, Ulf Wickström, Anja Geburtig, Peter Trubiroha, Volker Wachtendorf

16. Performance Control: Nondestructive Testing and Reliability Evaluation

Abstract
The performance of materials – as constituents of the components of engineering systems – is essential for the functionality of engineering systems in all branches of technology and industry. Instrumental for characterizing the performance of materials are
1.
methods to study and assess the basic damage mechanisms that detrimentally influence the proper functioning of materials, such as materials fatigue and fracture (Chap. 7), corrosion (Chap. 12), friction and wear (Chap. 13), biogenic impact (Chap. 14), materials–environment interactions (Chap. 15)
 
2.
methods to study and assess the performance of materials in engineering applications and to support condition monitoring of materialsʼ functional behavior.
 
In this chapter the following experimental and theoretical methods for performance control and condition monitoring are compiled.
  • Nondestructive evaluation (NDE) methods
  • Methods of industrial radiology
  • Methods of computed tomography (CT)
  • Embedded sensors techniques to monitor structural health and to assess materials performance in situ under application conditions
  • Methods to characterize the reliability of materials with statistical tools and test strategies for structural components and complex engineering systems.
Uwe Ewert, Gerd-Rüdiger Jaenisch, Kurt Osterloh, Uwe Zscherpel, Claude Bathias, Manfred P. Hentschel, Anton Erhard, Jürgen Goebbels, Holger Hanselka, Bernd R. Müller, Jürgen Nuffer, Werner Daum, David Flaschenträger, Enrico Janssen, Bernd Bertsche, Daniel Hofmann, Jochen Gäng

Modeling and Simulation Methods

Frontmatter

17. Molecular Dynamics

Abstract
This chapter gives an overview of the molecular dynamics (MD) simulation method. In the first section, the basics techniques of MD will be introduced so that the reader is able to start actual calculations. In the following three sections, several applications of MD simulation, some adapted for actual materials and others concerned with idealized model systems, will be presented. In the second section, a simulation study of diffusionless transformations such as the martensitic transformation and solid-state amorphization is presented. Analysis of amorphous and crystalline structures is described in Chap. 5 in this handbook. MD calculations of the processes involved in the preparation of amorphous alloys by rapid solidification as well as annealing processes in these alloys are discussed in the third section. In the last section, the investigation of atomic diffusion processes in liquid and solid (crystalline and amorphous) phases by MD simulation is explored. Readers may also refer to Chap. 7 concerning atomic diffusion processes in materials.
Masato Shimono

18. Continuum Constitutive Modeling

Abstract
Constitutive models play an important role when characterizing structural materials in order to evaluate their thermomechanical behavior. The experimental characterization of materials (using techniques discussed in Part C of this Handbook) involves measuring and controlling macroscopic variables such as force, displacement and temperature. Concise models are also of great use when characterizing the continuous media used to create structural materials, because phenomenological modeling can be carried out regardless of the internal material structure. This continuum modeling usually successfully describes the behavior of various classes of material under complex boundary conditions.
This chapter presents phenomenological constitutive models from both macroscopic and microscopic viewpoints:
  • Starting from viscoplasticity models, model performance is reviewed in order to predict the mechanical response under creep–plasticity interaction conditions, taking into account internal state variables.
  • Material anisotropy is discussed; mathematical modeling of initial anisotropy and induced anisotropy based on the representation theorem for higher order isotropic tensors is presented.
  • Thermomechanical coupling phenomena involving phase transformations predominatein engineering applications of heat treatment and material processing. A continuum model is presented that takes into account the way structural rearrangement evolves in materials.
  • Finally, microscopic analysis based on crystal plasticity, which relates the resolved shear stress to crystal slip, is applied to describe the inhomogeneous deformation process in polycrystalline materials.
Shoji Imatani

19. Finite Element and Finite Difference Methods

Abstract
Finite element methods (FEM) and finite difference methods (FDM) are numerical procedures for obtaining approximated solutions to boundary-value or initial-value problems. They can be applied to various areas of materials measurement and testing, especially for the characterization of mechanically or thermally loaded specimens or components. (Experimental methods for these fields have been treated in Chaps. 7 and 8.)
The principle is to replace an entire continuous domain of a body of interest by a number of subdomains in which the unknown function is represented by simple interpolation functions with unknown coefficients. Thus, the original boundary-value problem with an infinite number of degrees of freedom is converted into a problem with a finite number of degrees of freedom approximately.
Akira Tezuka

20. The CALPHAD Method

Abstract
Phase diagrams offer various areas of materials science and technology indispensable information for the comprehension of the properties of materials. The microstructure of solid materials is generally classified according to the size of the constituents – for example, at the electron, atomic, or granular level (Sect. 1.3). Accordingly, fundamental principles like quantum mechanics, statistical mechanics, or thermodynamics are applied individually to describe the physical properties. Phases are important features of material because they characterize homogeneous aggregations of matter with respect to chemical composition and uniform crystal structure. The various functions of a material are closely related to the phases and structures of the materialʼs composition. Therefore, to develop a material with a maximum level of desired functions, it is essential to undertake design of the structure in advance.
Phase diagrams are composed by means of experimental measurements, as well as statistical thermodynamic analysis. The construction of phase diagram calculations based on experiments and thermodynamic analysis are generally referred to as the calculation of phase diagrams (CALPHAD) approach [20.1]. This method provides a very accurate understanding of the properties originating in the macroscopic character of the material under study.
This chapter is organized in three parts:
  • In the first part, a brief outline of the CALPHAD method is summarized.
  • In the second part, the method for deriving the Gibbs free energies incorporating the ab initio calculations is presented in order to clarify the uncertainty of thermodynamic properties for metastable solution phases, taking the Fe–Be-based bcc phase as an example. Some results
for metastable phase equilibria in the Fe–Be,
and Co–Al binary systems are shown.
  • In the third part the application to predict thermodynamic properties of compound phases is discussed. The thermodynamic modeling for the Perovskite carbide with an E21-type structure in the Fe–Al–C, Co–Al–C and Ni–Al–C ternary systems is illustrated, and constructions of phase diagrams are performed.
Hiroshi Ohtani

21. Phase Field Approach

Abstract
The term phase field has recently become known across many fields of materials science. The meaning of phase field is the spatial and temporal order parameter field defined in a continuum-diffused interface model. By using the phase field order parameters, many types of complex microstructure changes observed in materials science are described effectively. This methodology has been referred to as the phase field method, phase field simulation, phase field modeling, phase field approach, etc. In this chapter, the basic concept and theoretical background for the phase field approach is explained in Sects. 21.1 and 21.2. The overview of recent applications of the phase field method is demonstrated in Sects. 21.3 to 21.6.
Phase field models have been successfully applied to various materials processes including solidification, solid-state phase transformations and microstructure changes. Using phase field methodology, one can deal with the evolution of arbitrary morphologies and complex microstructures without explicitly tracking the positions of interfaces. This approach can describe different processes such as diffusion-controlled phase separation and diffusionless phase transition within the same formulation. It is rather straightforward to incorporate the effect of coherency and applied stresses, as well as electrical and magnetic fields.
Since phase field methodology can model complex microstructure changes quantitatively, it will be possible to search for the most desirable microstructure using this method as a design simulation, i.e., through computer trial-and-error testing. Therefore, the most effective strategy for developing advanced materials is as follows. First, we elucidate the mechanism of microstructure changes experimentally, then we model the microstructure evolutions using the phase-field method based on the experimental results, and finally we search for the most desirable microstructure while simultaneously considering both the simulation and experimental data.
Toshiyuki Koyama

22. Monte Carlo Simulation

Abstract
In the general overview on materials and their characteristics, outlined in Sect. 1.3, it has been stated that materials and their characteristics result from the processing of matter. Thus, condensed matter physics is one of the fundamentals for the understanding of materials. The Monte Carlo Method, which is a powerful method in this respect, is presented in this final chapter of the Handbookʼs Part E on Modelling and Simulation Methods as follows:
First, the principles of this simulation technique are introduced
  • Monte Carlo Method: the fundamentals
  • Improved Monte Carlo algorithms
  • Quantum Monte Carlo Method.
Second, the application of the Monte Carlo Method is explained in considering selected areas of materials science.
  • Electronic correlations: antiferromagnetism
  • Perfect conductance of electricity: superconductivity
  • Vortex states in condensed matter physics
  • Quantum critical phenomena.
Xiao Hu, Yoshihiko Nonomura, Masanori Kohno

Backmatter

Additional information

Premium Partners

    Image Credits